What, if anything, should I change in the BIOS after building my computer? Are there any settings that I need to worry about if I'm not overclocking initially?
Not really, generally default BIOS settings are good enough for most people.
Some people might want to change the boot order or sata operation mode. Unless you have a reason for wanting to change the BIOS, don't.
often the RAM is running at 1333 in the BIOS even if it is rated at 1600/1866 or higher.
you may have to change the memory profile to get it to run at its design speed